Point B : surface (2007-2022)

Utilisation of : na_seadec() function
= Removes the seasonal component from the time series, performs imputation on the deseasonalized series and afterwards adds the seasonal component again.

Temperature & salinity

Other methods:

By autocorrelation + decompose function or Mann-Kendall : not possible because of gaps

–> Filling gaps.

Moving average

Temperature

## 
## Call:
## lm(formula = y ~ x, data = reg_val_ts_temp_som_less_season)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.2143 -1.3761 -0.0379  1.2627  7.3816 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 18.17497    0.16215 112.086  < 2e-16 ***
## x            0.06879    0.01629   4.224 2.67e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.137 on 832 degrees of freedom
## Multiple R-squared:  0.02099,    Adjusted R-squared:  0.01981 
## F-statistic: 17.84 on 1 and 832 DF,  p-value: 2.671e-05

Slope is 0.069.

Salinity

## 
## Call:
## lm(formula = y ~ x, data = reg_val_ts_sal_som_less_season)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.27358 -0.08520  0.05114  0.17007  0.43699 
## 
## Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept) 37.9500975  0.0211116 1797.592   <2e-16 ***
## x           -0.0001388  0.0020841   -0.067    0.947    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2787 on 832 degrees of freedom
## Multiple R-squared:  5.329e-06,  Adjusted R-squared:  -0.001197 
## F-statistic: 0.004434 on 1 and 832 DF,  p-value: 0.9469

Slope is 0.

Oxygen

## 
## Call:
## lm(formula = y ~ x, data = reg_val_ts_oxy_som_less_season)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -52.554 -13.868   0.713  14.278  58.247 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 231.1150     1.3735 168.273  < 2e-16 ***
## x             0.4599     0.1520   3.025  0.00256 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.92 on 832 degrees of freedom
## Multiple R-squared:  0.01088,    Adjusted R-squared:  0.009691 
## F-statistic: 9.152 on 1 and 832 DF,  p-value: 0.002561

Slope is 0.46.

AOU

## 
## Call:
## lm(formula = y ~ x, data = reg_val_ts_aou_som_less_season)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -49.333  -8.959  -1.327   7.272  63.330 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.528809   0.972700  -1.572    0.116    
## x           -0.044808   0.006033  -7.427 2.75e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.98 on 832 degrees of freedom
## Multiple R-squared:  0.06218,    Adjusted R-squared:  0.06105 
## F-statistic: 55.16 on 1 and 832 DF,  p-value: 2.753e-13

Slope is -0.045.

pH spectro

## [1] 52

## 
## Call:
## lm(formula = y ~ x, data = reg_val_ts_ph_som_less_season)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.091919 -0.008087  0.000901  0.008464  0.053927 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  8.0871235  0.0017723 4562.94   <2e-16 ***
## x           -0.0037125  0.0003217  -11.54   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01521 on 415 degrees of freedom
## Multiple R-squared:  0.243,  Adjusted R-squared:  0.2412 
## F-statistic: 133.2 on 1 and 415 DF,  p-value: < 2.2e-16

Slope is -0.0037.

pH spect 25°C

## 
## Call:
## lm(formula = y ~ x, data = reg_val_ts_ph25_som_less_season)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.065216 -0.006559  0.000560  0.007624  0.030494 
## 
## Coefficients:
##               Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)  7.9754409  0.0016366 4873.054   <2e-16 ***
## x           -0.0008251  0.0003530   -2.338     0.02 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01218 on 336 degrees of freedom
## Multiple R-squared:  0.016,  Adjusted R-squared:  0.01307 
## F-statistic: 5.464 on 1 and 336 DF,  p-value: 0.01999

Slope is -8^{-4}.

AT

  • Data before 2022-09-28.

## 
## Call:
## lm(formula = y ~ x, data = reg_val_ts_ta_som_less_season)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -55.012  -7.174   0.744   7.972  34.467 
## 
## Coefficients:
##              Estimate Std. Error  t value Pr(>|t|)    
## (Intercept) 2.550e+03  9.480e-01 2690.196  < 2e-16 ***
## x           5.397e-01  9.505e-02    5.678 1.89e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.39 on 818 degrees of freedom
## Multiple R-squared:  0.03792,    Adjusted R-squared:  0.03675 
## F-statistic: 32.24 on 1 and 818 DF,  p-value: 1.89e-08

DIC

  • Data before 2022-09-29.

## 
## Call:
## lm(formula = y ~ x, data = reg_val_ts_dic_som_less_season)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -56.041  -7.370  -0.436   6.962  49.663 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2227.8511     1.0381 2146.09   <2e-16 ***
## x              2.3996     0.1059   22.66   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.54 on 818 degrees of freedom
## Multiple R-squared:  0.3856, Adjusted R-squared:  0.3849 
## F-statistic: 513.5 on 1 and 818 DF,  p-value: < 2.2e-16

Slope is 2.3996.

pCO2

  • pCO2 from 2007-01 to 2008-12.
  • pCO2_w from 2009-01 to 2022-09.
  • pCO2_atmos from 2009-01 to 2021-12
  • NpCO2 from 2009-01 to 2022-09.
  • TpCO2 from 2009-01 to 2022-12.

## 
## Call:
## lm(formula = y ~ x, data = reg_val_ts_npco2_som_less_season)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -63.639 -10.793  -0.726   9.541  73.760 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 380.6386     1.4597  260.77   <2e-16 ***
## x             3.8944     0.1738   22.41   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.03 on 676 degrees of freedom
## Multiple R-squared:  0.4263, Adjusted R-squared:  0.4254 
## F-statistic: 502.3 on 1 and 676 DF,  p-value: < 2.2e-16

Slope is 3.8944.

## 
## Call:
## lm(formula = y ~ x, data = reg_val_ts_tpco2_som_less_season)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -102.260  -10.129   -0.884   11.125   90.660 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 408.6197     1.7157 238.170  < 2e-16 ***
## x             1.3717     0.1911   7.177 1.76e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.93 on 728 degrees of freedom
## Multiple R-squared:  0.06608,    Adjusted R-squared:  0.0648 
## F-statistic: 51.51 on 1 and 728 DF,  p-value: 1.759e-12

Slope is 1.3717.

Mann-Kendall

  • The function kendall.SeasonalTrendTest returns estimated values of Kendall’s τ, the slope, and the intercept for each season, as well as a single estimate for each of these three quantities combined over all seasons. The overall estimate of τ is the weighted average of the p seasonal τ’s

  • The overall estimate of slope is the median of all two-point slopes computed within each season.

  • The overall estimate of intercept is the median of the p seasonal estimates of intercept.


  • The Kendall Tau, or Kendall rank correlation coefficient, measures the monotony of the slope. Kendall’s Tau varies between -1 and 1; it is positive when the trend increases and negative when the trend decreases.

  • The Sen slope, which estimates the overall slope of the time series. This slope corresponds to the median of all the slopes calculated between each pair of points in the series.

  • The significance, which represents the threshold for which the hypothesis that there is no trend is accepted. The trend is statistically significant when the p-value is less than 0.05.

Results:

Temperature

##         tau       slope   intercept 
##   0.1706592   0.0588000 -95.1549068

Salinity

##          tau        slope    intercept 
##  0.120366159  0.008733333 17.433617625

Oxygen

##           tau         slope     intercept 
##    0.06463341    0.19334433 -103.85815454

AOU

##         tau       slope   intercept 
##  -0.1435331  -0.3892117 681.3424309

pH spectro

##          tau        slope    intercept 
## -0.315104877 -0.003043814 13.820156485

pH spectro 25°C

##          tau        slope    intercept 
## -0.108828665 -0.001062714  9.451001988

TA

##          tau        slope    intercept 
##    0.1537045    0.7121110 1068.9098590

DIC

##           tau         slope     intercept 
##     0.4768069     2.5655170 -3083.4315360

NpCO2

##           tau         slope     intercept 
##     0.4888721     3.7316570 -6721.4398537

TpCO2

##           tau         slope     intercept 
##     0.1706592     0.9313975 -1209.3123620